Because the returns are not good.
One of the big drivers in Australia is "negative gearing": if your investment loses money you can offset losses against your tax on other income. Institutional investors and corporations are in the business of making money: not losing it. Housing market investors are betting that these year to year revenue losses will ultimately be made up in a big capital gain: for which individuals get a huge tax break that is also not available to corporations.
Capital gains are not guaranteed. Australia has benefited from 25+ years of economic, employment and wages growth: a result of good government planning, strong corporate governance and a fair slice of luck. If this were to end housing prices would plateau at best and crash at worst. A person who has negative cash flow investments has to sell them urgently if they lose their job. A glut of mortgagee sales and property prices could easily come off 20-30%.
Rental yields on residential property in Sydney are about 4% with a capital gain of currently 10% but this has been flat or negative within the last 5 years and no doubt will be again within the next 5. Rental yields for residential property are constrained by mortgage rates: if it significantly cheaper to buy then to rent, why would anyone rent?
In contrast, industrial and commercial property gets a yield of about 7% and gets exactly the same capital gain. This is because land is land and if the price of industrial land doesn't grow at the same rate as the residential land next door eventually one will be converted into the other. Retail rentals are even higher. In addition commercial tenants are responsible for more outgoings and have fewer legal rights than residential tenants.
Further, individual residential properties are horribly illiquid and have large transaction costs. While it is possible to bundle them up into property trusts so that units can be sold on the stock exchange it is far more common to do this with office and retail buildings. This is what companies like Westfield and AMP Capital do. Notwithstanding, heavily geared property trusts can get into deep water because of the illiquid nature of property as the failure of Centro illustrates.
That said, there are plenty of companies that develop residential houses and units for sale to owner occupiers or investors because that's where the money is.